VGChartz teaches me mathzz: Precalculus edition

[hatmoza]

Soriku said:

So I don't understand my homework and VGC is going to help me out (hopefully). I'll do 2 questions at a time but I have 5 (although I have one more question non homework I have a question in). Btw Precalc sucks. I pay attention in class and still have no idea what to do...

1. The number of horsepower H required to overcome wind drag on an automobile is approximated by the model:

H(x) = 0.002x^2 0.005x - 0.029, 10 < x < 100

where x is the speed of the car in miles per hour.

Rewrite the function so that x represents speed in kilometers per hour [Find H(x/1.6).] Describe the transformation applied to the graph of the function.

2. Find the domain of the function: f(x)= -2x - 4 (note that there's a square root sign over -2x - 4)

I know the answer is (-Infinity, -2] but I don't understand how you get the answer.

My calculus is a little rusty (haven't taken it in years)

But I think I can help you out with the second one.

Remember f(x) is basically y (think axis)

first thing you want to do is zero out the equation in the square root because nothing in a square root is allowed to be negative

 

so it will look like this    0=-2x-4

then solve for x 

4 = -2x which is x= -2   that's half the answer.

Remember: nothing in a square root can be negative.

if you replace x with -2, inside the square would be 0, the tipping point between positive and negative. so we're on the right path.

so we know the domain either starts or ends at -2

now lets see what happens if we put -1 or negative -3 to see where the inside of the square root stays positive,and if the domain heads to the more negative side or positive.  

if we put -1 (which is going towards positive infinity), inside the square root will be  -2 !! But we want the inside of the square root to remain positive so we know it's not going towards positive infinty.

Lets replace x with -3. What is the inside of the root equal to now? it equals 2 Bingo!

so the ending point is -2 when we zero out the root.

if we replace x with numbers that are heading torwards negative infinity, the inside of the square root remains positive.

So the domain is (-infinity, -2)